Body measurements of American boys and girls for garment and pattern construction; a comprehensive report of measuring procedures and statistical analysis of data on 147,000 American children,

Contribution from Bureau of home economics in cooperation with Works progress administration.

Statistical Analysis of Data on Linker Histones/DNA Interactions

2000 Mathematics Subject Classification: 62P10, 92C40

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as “histogram binning” inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. ^ Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. ^ The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. ^ These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. ^ In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation. ^

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as "histogram binning" inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation.

Does time ever fly or slow down? The difficult interpretation of psychophysical data on time perception.

Time perception is studied with subjective or semi-objective psychophysical methods. With subjective methods, observers provide quantitative estimates of duration and data depict the psychophysical function relating subjective duration to objective duration. With semi-objective methods, observers provide categorical or comparative judgments of duration and data depict the psychometric function relating the probability of a certain judgment to objective duration. Both approaches are used to study whether subjective and objective time run at the same pace or whether time flies or slows down under certain conditions. We analyze theoretical aspects affecting the interpretation of data gathered with the most widely used semi-objective methods, including single-presentation and paired-comparison methods. For this purpose, a formal model of psychophysical performance is used in which subjective duration is represented via a psychophysical function and the scalar property. This provides the timing component of the model, which is invariant across methods. A decisional component that varies across methods reflects how observers use subjective durations to make judgments and give the responses requested under each method. Application of the model shows that psychometric functions in single-presentation methods are uninterpretable because the various influences on observed performance are inextricably confounded in the data. In contrast, data gathered with paired-comparison methods permit separating out those influences. Prevalent approaches to fitting psychometric functions to data are also discussed and shown to be inconsistent with widely accepted principles of time perception, implicitly assuming instead that subjective time equals objective time and that observed differences across conditions do not reflect differences in perceived duration but criterion shifts. These analyses prompt evidence-based recommendations for best methodological practice in studies on time perception.

Sensitivity analysis for unmeasured confounders using an electronic spreadsheet

In studies assessing the effects of a given exposure variable and a specific outcome of interest, confusion may arise from the mistaken impression that the exposure variable is producing the outcome of interest, when in fact the observed effect is due to an existing confounder. However, quantitative techniques are rarely used to determine the potential influence of unmeasured confounders. Sensitivity analysis is a statistical technique that allows to quantitatively measuring the impact of an unmeasured confounding variable on the association of interest that is being assessed. The purpose of this study was to make it feasible to apply two sensitivity analysis methods available in the literature, developed by Rosenbaum and Greenland, using an electronic spreadsheet. Thus, it can be easier for researchers to include this quantitative tool in the set of procedures that have been commonly used in the stage of result validation.

Some reflections on acquisition, processing and analysis of statistical data in forest soils

Beyond the classical statistical approaches (determination of basic statistics, regression analysis, ANOVA, etc.) a new set of applications of different statistical techniques has increasingly gained relevance in the analysis, processing and interpretation of data concerning the characteristics of forest soils. This is possible to be seen in some of the recent publications in the context of Multivariate Statistics. These new methods require additional care that is not always included or refered in some approaches. In the particular case of geostatistical data applications it is necessary, besides to geo-reference all the data acquisition, to collect the samples in regular grids and in sufficient quantity so that the variograms can reflect the spatial distribution of soil properties in a representative manner. In the case of the great majority of Multivariate Statistics techniques (Principal Component Analysis, Correspondence Analysis, Cluster Analysis, etc.) despite the fact they do not require in most cases the assumption of normal distribution, they however need a proper and rigorous strategy for its utilization. In this work, some reflections about these methodologies and, in particular, about the main constraints that often occur during the information collecting process and about the various linking possibilities of these different techniques will be presented. At the end, illustrations of some particular cases of the applications of these statistical methods will also be presented.

Stratigraphic interpretation of Well-Log data of the Athabasca Oil Sands of Alberta Canada through Pattern recognition and Artificial Intelligence

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Interpretation of array comparative genome hybridization data: a major challenge.

The advent and application of high-resolution array-based comparative genome hybridization (array CGH) has led to the detection of large numbers of copy number variants (CNVs) in patients with developmental delay and/or multiple congenital anomalies as well as in healthy individuals. The notion that CNVs are also abundantly present in the normal population challenges the interpretation of the clinical significance of detected CNVs in patients. In this review we will illustrate a general clinical workflow based on our own experience that can be used in routine diagnostics for the interpretation of CNVs.